Modeling of the radiative contribution to heat transfer in porous media composed of spheres or cylinders

A theoretical model for evaluating the radiative conductivity tensor of a porous media is developed in this paper. The porous media is composed of a transparent fluid and opaque particles with characteristic lengths longer than the radiation wavelength. The main features of the proposed approach are (i) take into account the interaction between conduction and radiation heat transfers, (ii) allow the modeling of the radiative transfer in anisotropy system such as an assembly of cylinders, and (iii) have an easy numerical implementation into the energy equations of the porous media. In order to study the accuracy of the approach, the paper evaluates the model for porous media composed of spheres or cylinders. The predictions of the model agree well with experimental data and with results obtained from finite element simulations. The numerical results also show that the radiative conductivity can be strongly influence by the effect of temperature distribution across the particle surface and by the effect of the multiple scattering of radiation in the porous media.     

Numerical study of phonon radiative transfer in porous nanostructures

This study analyzes the phonon radiative transfer in two-dimensional porous silicon nanostructures with a phonon transport model based on the Boltzmann transportation equation. We focus on the inter-scattering between pores. The numerical results show that when the aspect ratio is less than 1.22, the scale factor dominates the thermal conductivity, and the thermal conductivity of nanostructures with in-line arrangement pores is determined by the dependent phonon scattering effect. In nanostructures with staggered arrangement pores, the phonons are prevented from transporting through the material. In general, the results show that the larger the pore size, the lower the thermal conductivity of the nanostructure. The results presented in this study provide a useful reference for the development of high-efficiency thermoelectric structures.     

Scaling anisotropic scattering in radiative transfer in three-dimensional nonhomogeneous media

Radiative heat transfer in three-dimensional nonhomogeneous participating medium was investigated by using REM² method. The anisotropic scattering phase function was dealt with the scaling technique based on delta function approximation. The three-dimensional scaled isotropic results were compared with the published anisotropic scattering computations. A good agreement between the scaled isotropic approaches and the anisotropic solutions was found. The effects of scattering albedo, forward fraction of phase function, and wall emissivity were discussed. It was found that, with the increase of the scattering albedo, the radiative heat flux increases for forward scattering media, but decreases for backward scattering media. The radiative heat flux is increased with the increases of forward fraction of phase function and wall emissivity. The emissive power at the center of a cubical nonhomogeneous medium in radiative equilibrium with gray diffuse walls equals to the averaged blackbody emissive power of the six walls.     

A general bioheat transfer model based on the theory of porous media

A volume averaging theory (VAT) established in the field of fluid-saturated porous media has been successfully exploited to derive a general set of bioheat transfer equations for blood flows and its surrounding biological tissue. A closed set of macroscopic governing equations for both velocity and temperature fields in intra- and extravascular phases has been established, for the first time, using the theory of anisotropic porous media. Firstly, two individual macroscopic energy equations are derived for the blood flow and its surrounding tissue under the thermal non-equilibrium condition. The blood perfusion term is identified and modeled in consideration of the transvascular flow in the extravascular region, while the dispersion and interfacial heat transfer terms are modeled according to conventional porous media treatments. It is shown that the resulting two-energy equation model reduces to Pennes model, Wulff model and their modifications, under appropriate conditions. Subsequently, the two-energy equation model has been extended to the three-energy equation version, in order to account for the countercurrent heat transfer between closely spaced arteries and veins in the circulatory system and its effect on the peripheral heat transfer. This general form of three-energy equation model naturally reduces to the energy equations for the tissue, proposed by Chato, Keller and Seiler. Controversial issues on blood perfusion, dispersion and interfacial heat transfer coefficient are discussed in a rigorous mathematical manner.     

Theory of near-field radiative heat transfer for stratified magnetic media

We report a general model to deal with near-field radiative heat transfer for the layered magnetic media, which is also applicable for layered nonmagnetic media. In the derivation, a method using the reciprocity theorem with dyadic Green’s function (DGF) and transfer matrix is introduced, which make the expressions simple and compact. By means of multiple reflection diagrams, it is clear to understand the physical interpretation of DGF and it is easy to evaluate it with physical picture for simple construction. Finally, the expression for the near-field radiative heat transfer between two semi-infinite solids separated by a medium is given as an example. Some numerical computations are conducted for both non-magnetic and magnetic media, which reveals the validity of the derived expressions and the difference between the two types of materials from the point of view of near-field radiative heat transfer. Furthermore, the results indicate that the near-field radiative flux will be further enhanced by excitation of surface polaritons in TE polarization for magnetic media.     

Generalized radiative transfer equation for porous medium upscaling: Application to the radiative Fourier law

Many porous media cannot be homogenized as Beerian semi-transparent media. Effective extinction, absorption and scattering coefficients can indeed have no physical meaning for small or intermediate optical thicknesses. A generalized radiative transfer equation (GRTE), directly based on the extinction cumulative distribution function, the absorption and scattering cumulative probabilities and the scattering phase function is established for this optical thickness range. It can be solved by a statistical Monte Carlo approach. For a phase of a porous medium that is optically thick at local scale, the GRTE degenerates into a classical Beerian RTE. In these conditions, a radiative conductivity tensor is directly obtained, by a perturbation method, and expressed with the radiative coefficients of this RTE and temperature. As illustrations, exhaustive radiative conductivity results are given for a set of overlapping transparent spheres within an opaque phase and for opaque rod bundles.     

Natural convection with coupled mass transfer in porous media

For certain types of packed beds used for thermal energy storage, high discharge rates can be achieved if the effective conductance is increased over that achievable with stagnant gases and liquids. A packed bed containing a fluid mixture with one condensing component and with the fluid mixture simultaneously convecting may achieve the required high conductances.An analogy has been developed with a similar system with no coupled mass transfer. It provides some useful insights into the role of gas/vapour mixture properties on the effective conductivity of such systems, and suggests that very large increases in effective conductivity are achievable.     

Transient coupled radiative and conductive heat transfer in a composite of semitransparent media

INTRODUCTIONIhsemitransparentmaterial(STM),energyisusuallytransferredbyradiationinaddihontoheatconduchon.WhenthesemitransparentmaterialisexPOsedtohightemperatUresurroundingsorwhenanintensiveincidentradiationexists,theeffectoftheradiationonthetransienttempef~fieldsismoreimpobotthanthat'oftheconduchon.msfeatUreplaysanimpoftalltroleinmanufactUreandengineeringaPPlicationsofalotofsemitransparentnderialsll],suchasglassindustry,ceramicandfiber~rials,mulh-layersemiconductors,moltensaltmedia,se…     

Double porous media model for mass transfer of hemodialyzers

Double porous media model for mass transfer of hollow fiber hemodialyzers is presented. In the model, the hollow fiber bundle is treated as a porous region composed of two interpenetrating porous regions i.e. the blood and dialysate flow regions, and the interface of the two regions is the porous membrane through which mass transfer is performed. Navier-Stokes equations with Darcy source terms are used to describe the flows within the two regions. Modified Kedem-Katchalsky equations as other source terms are added into conservation equations to simulate the permeating flux through the porous membrane. The model is validated with respect to the experimental data in the literature.     

Radiative heat transfer in porous media with spatially-dependent heat generation

We report an investigation of radiative heat transfer in porous radiant burners. The combustion was modeled as a spatially-dependent heat generation. Using the spherical harmonics to solve the equation of transfer, we have obtained the P-11 solution for the net radiative heat flux. Results presented illustrate the radiant output as a function of the position of the combustion zone, the optical thickness and the type of scattering of the porous layer, and the amount of reflection from the distribution chamber.     

高温下多孔体中的传热

叙述了多孔体中高温气体焓和辐射能转换的基本原理;并介绍了目前在几个方面的应用例和取得的实际效果。     

Chebyshev collocation spectral method for one-dimensional radiative heat transfer in graded index media

Chebyshev spectral collocation method based on discrete ordinates equation is developed to solve radiative transfer problems in a one-dimensional absorbing, emitting and scattering semitransparent slab with spatially variable refractive index. For radiative transfer equation, the angular domain is discretized by discrete ordinates method, and the spatial domain is discretized by Chebyshev collocation spectral method. Due to the exponential convergence of spectral methods, a very high accuracy can be obtained even using few nodes for present problems. Numerical results by the Chebyshev collocation spectral-discrete ordinates method (SP-DOM) are compared with those available data in references. Effects of refractive index gradient on radiative intensity are studied for space dependent scattering media. The results show that SP-DOM has a good accuracy and efficiency for solving radiative heat transfer problems in even spatially varying absorbing, emitting, scattering, and graded index media.     

On the discrete ordinates method for radiative heat transfer in anisotropically scattering media

In the discrete ordinates method (DOM), the normalized condition for the numerical quadrature of some complex scattering phase functions may not be satisfied. In this paper, a revised discrete ordinates method (RDOM) is developed to overcome this problem, in which a renormalizing factor is added into the numerical quadrature of in-scattering term. The RDOM is used to solve the radiative transfer problem in one-dimensional anisotropically scattering media with complex phase function. The radiative heat fluxes obtained by the RDOM are compared with those obtained by the conventional discrete ordinates method (CDOM) and Monte Carlo method. The results show the RDOM can overcome the false scattering resulted from the numerical quadrature of in-scattering term and improve largely the accuracy of solution of the radiative transfer equation by comparison with the CDOM.     

Analysis of heat transfer for compressible flow in two-dimensional porous media

Gas from a reservoir at constant pressure and temperature is forced through a two-dimensional porous region. The surface through which the gas exits is at a specified uniform temperature and pressure. The local gas and solid matrix temperatures are assumed equal. General solutions for the local temperature and pressure in the porous medium are found as a function of a potential. This potential can be determined by solving Laplace's equation in the porous region for a simple set of boundary conditions, and the temperature and pressure will then be known functions of position. Because of the nature of the boundary conditions it is particularly convenient to solve Laplace's equation by conformai mapping. By using this technique some illustrative heat and mass flow results were calculated for a porous wall with a step in thickness, a wall supplied with gas through periodic slots, and an eccentric annular region.     

多孔介质对冷热流体横向射流混合过程热波动的影响

运用流固耦合方法建模,应用FLUENT计算软件平台对填充有多孔介质的T型连接方形管道内冷热流体横向射流混合过程的流动和热传递进行大涡模拟,采用了Smagorinsky-Lilly亚格子模型,获得了瞬时速度和温度分布.结果表明,填充多孔介质能够有效减少T型连接管道中冷热流体横向射流混合的温度和速度波动.固体骨架的导热率较...     

The theory of heat and moisture transfer in porous media revisited

In this paper a review is presented of the present status of the theory of combined heat and moisture transfer in porous media, developed by J. R. Philip and the author in the mid-1950s. First, attention is drawn to the limitations of the theory and the assumptions underlying it. Next, attempts to test the theory by laboratory and field experiments are briefly discussed, leading to the conclusion that the usefulness of the theory in describing and analysing the experiments was proven, but that doubts remain about its predictive value. These doubts are a consequence of: (a) the limitations of the theory; (b) uncertainty about the quality of the experimental procedures and data. Remarks are made on hysteresis and its possible influence. It is concluded that experiments aimed at a study of the behaviour of nonisothermal systems subjected to hysteresis are needed. Finally, the problem of the definition and use of an apparent thermal conductivity is analysed. In the original papers two alternatives were presented. An expression for the phase average of the vapour flux density is derived. A numerical example is presented and suggestions are made concerning the proper choice between the alternatives.     

A new approach to solve the radiative transfer equation in plane-parallel semitransparent media with variable refractive index based on the discrete transfer method

The radiative transfer equation in plane-parallel semitransparent media with variable refractive index is solved by the discrete transfer method. The medium refractive index is assumed to be constant in each control volume, such that the rays travel straight lines in control volumes, and redirect at interfaces. The effects of medium's refractive index on the curvature of solid angles are considered by a new set of weights, which are dependent on both ray path and medium's refractive index. The results are verified by comparing with a benchmark problem and the performance of the method is examined by various examples.